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Noncooperative Game TheoryAn Introduction for Engineers and Computer Scientists$
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João P. Hespanha

Print publication date: 2017

Print ISBN-13: 9780691175218

Published to Princeton Scholarship Online: May 2018

DOI: 10.23943/princeton/9780691175218.001.0001

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Computation of Nash Equilibria for Bimatrix Games

Computation of Nash Equilibria for Bimatrix Games

Chapter:
(p.118) Lecture 10 Computation of Nash Equilibria for Bimatrix Games
Source:
Noncooperative Game Theory
Author(s):

João P. Hespanha

Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691175218.003.0010

This chapter discusses the computation of the Nash equilibrium for bimatrix games. It begins by considering a different version of the battle of the sexes game introduced in Chapter 9, in which action 1 corresponds to going to the baby shower and action 2 to the football game. In this new version no one really wants to go to the football game alone (cost of 3), but going to the baby shower alone is a little better (cost of 0). After finding the mixed Nash equilibrium for this case, the chapter describes the computation of a completely mixed Nash equilibrium and the numerical computation of a mixed Nash equilibrium. It concludes with a practice exercise and the corresponding solution, along with an additional exercise.

Keywords:   bimatrix game, battle of the sexes, action, mixed Nash equilibrium, completely mixed Nash equilibrium

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